how to build a carriage that reacts to an uneven ground
I don't know if it will help, but here is a way to make wheels following the ground:


Create a cube (the vehicle), a wheel, and a small plane.
Parent the wheel and the plane to the cube.
Put the plane under your wheel, subdivide it a bit, assign a vertex group to the whole mesh.
Give it a Shrinkwrap modifier, choose the ground as the Target
Give your wheel a Copy Location constraint, choose the plane as Target, select the plane's vertex group in Vertex Group, deactivate the X and Y axis so that it only moves on the Z axis, activate Offset and place the wheel at its right position, on the ground and above the small plane.
Move the cube to test the animation, the wheel should follow the ground.
Copy paste x 4 the wheel + its plane.